Hatris!
VolfieV(D)!
Lode Runner: Lost Labrynth :-"
I don't have it but I would imagine Double Dragon II would be easily playable without any knowledge of Japanese.
Flash Hiders is a fighter and can be played without understanding the text. That goes for all the fighting games, Street Fighter II: CE', Art of Fighting, Fatal Fury 2, Fatal Fury Special, I'm sure there are others I'm not thinking of (I don't own or play many of 'em).
I see some PCE versions of US games listed, so here are a couple more of the Japanese counterparts that don't require any knowledge of the language: Crest of Wolf (Riot Zone), Pomping World (Buster Bros).
Altered Beast, though you'd need a V1 System card or a flash card to play the CD version.
Magicoal is somewhat text heavy, but it's still playable (and enjoyable). Same goes for Dungeon Explorer II and Neutopia II.
Also, the Tennokoe Bank is easy to figure out how to use and is an essential addition to any library.
If you want to go the extra mile, I've been using great walkthrus for FEOE: Kabuki Den and Dragon Knight III and have had no issues so far. The games have been very enjoyable to play with the walkthrus (found on gamefaqs). I've saved the text files to my computer, but if you'd like I could dig up the links on gamefaqs.